Entropy

Fréchet distribution differential entropy.

The differential entropy for a Fréchet random variable shape α > 0, scale s > 0, and location parameter m is

h left-parenthesis upper X right-parenthesis equals 1 plus StartFraction gamma Over alpha EndFraction plus gamma plus ln left-parenthesis StartFraction s Over alpha EndFraction right-parenthesis

where γ is the Euler–Mascheroni constant.

Usage

var entropy = require( '@stdlib/math/base/dists/frechet/entropy' );

entropy( alpha, s, m )

Returns the differential entropy for a Fréchet distribution with shape alpha > 0, scale s > 0, and location parameter m (in nats).

var y = entropy( 2.0, 1.0, 1.0 );
// returns ~1.173

y = entropy( 1.0, 1.0, -1.0 );
// returns ~2.154

y = entropy( 1.0, 1.0, 2.0 );
// returns ~2.154

If provided NaN as any argument, the function returns NaN.

var y = entropy( NaN, 1.0, -2.0 );
// returns NaN

y = entropy( 1.0, NaN, -2.0 );
// returns NaN

y = entropy( 1.0, 1.0, NaN );
// returns NaN

If provided alpha <= 0, the function returns NaN.

var y = entropy( 0.0, 3.0, 2.0 );
// returns NaN

y = entropy( 0.0, -1.0, 2.0 );
// returns NaN

If provided s <= 0, the function returns NaN.

var y = entropy( 1.0, 0.0, 2.0 );
// returns NaN

y = entropy( 1.0, -1.0, 2.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/math/float64-eps' );
var entropy = require( '@stdlib/math/base/dists/frechet/entropy' );

var alpha;
var m;
var s;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*20.0 ) + EPS;
    s = ( randu()*20.0 ) + EPS;
    m = ( randu()*20.0 ) - 40.0;
    y = entropy( alpha, s, m );
    console.log( 'α: %d, s: %d, m: %d, h(X;α,s,m): %d', alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
}